We need to perform the operations in the given expression according to the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction) to simplify the expression.
First, let's convert the mixed number 12 8/15 to an improper fraction. To do this, multiply the whole number (12) by the denominator (15) and add the numerator (8):
12 * 15 + 8 = 180 + 8 = 188.
Now, the expression is:
188/15 - 7 + 7/15 + 15.
Next, let's find a common denominator for the fractions. The common denominator is 15:
188/15 - 7 + 7/15 + 15/1.
Now we can add the fractions:
(188 + 7 + 7) / 15 + 15/1.
Simplifying further:
202 / 15 + 15/1.
The fractions have a common denominator, so we can add them:
(202 + 225) / 15.
Simplifying the numerator:
427 / 15.
Therefore, the expression 12 8/15 − 7 + 7/15 + 15 simplified to its simplest form is 427/15.